# Which factors influence the evaporation rate?

## Psychrometer

*Physical processes in ecology: evaporation*

**- evaporation -**

**Seminar and exercise**

**- Physical processes in ecology -**

Evaporation is the phase change from liquid water to water vapor. It is a crucial process both for the physical state of the atmosphere (weather, climate) and for the water supply of ecosystems (plants, soil).

If the atmosphere is only a few percent undersaturated, moist surfaces evaporate liquid water. Condensation is the reverse of evaporation. The direction of the transport depends on the sign of the difference in the chemical potentials between the initial and final state of the water, i.e., e.g. as liquid water in solutions such as surface water, apoplast solution in the cell walls of leaves or soil solution, or in the form of water vapor in the atmosphere. In the ecological area we are used to that **chemical potential of water **also simply as **Water potential**Ψ, to denote the difference between the water under tension and the free water. This difference is negative and is given as pressure (= energy / volume) in the unit Pa.

The chemical potential of water is closely related to that **relative humidity** together. Even a few% undersaturation of the atmosphere means a very strong negative chemical potential of a few MPa, i.e. much higher than that in the root zone of the soil or in the plant tissue. At the equilibrium end point, the change in chemical potential is zero. As a rule, however, the atmosphere does not reach this equilibrium. When it rains, the atmosphere usually remains m.o.w. very undersaturated.

### Evaporation I: From the psychrometer to the Penman equation

The **Flux density of the water vapor** of a water surface E (evaporation rate = rate of water vapor release per square meter per time) does not determine the difference in chemical potential, but the difference in water vapor partial pressure between the surface and a reference altitude and the conductivity of the atmosphere (*g = 1 / r*). The following considerations should give you an understanding of the control and quantitative description of evaporation.

In general, the following applies to the evaporation rate (water vapor flux density)

*r*as the transport resistance for water vapor, ρ

_{w}*the absolute humidity (ρ*

_{w}*= Water vapor density in kg / m³) and p*

_{w}_{L.}the air pressure in Pa (for an explanation of the symbols used, see also the instructions for the meteorological instrument internship, experiment 3). In the right term is the same fact for the water vapor partial pressure,

*e*shown in Pa. This has the advantage that we know the vapor pressure directly at the water surface:

The evaporation of water is not only a flow of matter but also an energy flow. The amount of energy used for evaporation is the product of evaporation and the heat of evaporation λ_{w}, or here simply λ, so it applies

_{w}has a value of approx. 2.5 MJ / kg as a good approximation and depends only slightly on the temperature.

The consideration of energy flows helps us to determine the transport quantities because we can now set up an energy balance equation with the help of the 1st law of thermodynamics (conservation of energy). Deviating from the energy balance equation known to you from the Bioclimatology I lecture, we use its internationally common form here:

*R.*for the net radiation,

_{n}*G*for the existing soil heat flow (positive energy increase) and λ

*E.*and

*H*for the latent and the sensible heat flow (both positive upwards) all sizes in W / m².

An expression similar to Equation 2 for

*H*is

*c*the specific heat capacity for air at constant pressure is (1004 J / (K kg)).

_{p}In preparation for the complicated situation in the tree population, we now look at the two thermometers of one **Psychrometers**. The psychrometer is an easy to understand model of one *adiabatic* Change of state in which energy flows between the air and the surface (wet or dry thermometer) can occur.

Set up equation 3 for the following situations and characterize their terms in relation to zero (>, = or <0).

- Dry thermometer before equilibrium is established (Eq. 5)
- Dry thermometer after equilibrium has been established (Eq. 6)
- Moisture thermometer after equilibrium has been set (Eq. 7)

*r*=

_{w}*r*.

_{H}This equation is used to calculate the current vapor pressure from the temperature difference between dry and wet thermometers of a psychrometer after equilibrium has been set. It tells us something about the extent to which, in the adiabatic case, the temperature on the surface falls through evaporation and the current vapor pressure increases in the process.

Withγ is the name of the psychrometer constant, it takes a value of 66 Pa / K at 20 ° C.

Let us now allow radiation and thus treat the more generally applicable, *diabatic * Fall as it is the rule in nature.

The difference between net radiation and heat storage (*Rn-G*, also known as available radiation energy) is now available for the latent and sensible heat flow. But how is this energy divided?

Set up the energy balance equation and thus make clear the approach to answering this question.

*Rn-G, r _{H}= r_{w}*,

*e*and

*T*are measurable quantities or can easily be derived from measurements. This is more difficult for the surface temperature

*T*

_{s}and the corresponding vapor pressure at the surface E

_{s}(T

_{s}).

An approach goes back to Penman (1948) with which the surface temperature can be approximated (equation in Fig. 3).

If one uses this approximation for the surface moisture and solves the energy balance equation for the latent heat flow, the so-called Penman equation results as

. (Eq. 10)

With Eq. 10 you can determine the evaporation of a "free" water surface, e.g. a forest covered with rainwater. This size is also known as potential evaporation. The difference between precipitation and potential evaporation, the so-called atmospheric water balance, is calculated as an indicator for the water supply from general weather data.

*Penman, H.L. (1948): Natural evaporation from open water, bare soil and grass. Proc. Roy. Soc. London A (194), 120-145.*

### Evaporation II: Penman-Monteith equation and energy balance of forest stands

The current evaporation is not always the same as the potential evaporation, since plant populations regulate transpiration via the stomata (guard cells of the leaves). Monteith (1968) extended Eq. 10 to the modified Penman-Monteith equation by integrating the stomata resistance of the stand into the equation. This approach is the classic case of a "*big leaf "*-Model: the stock is treated like a single large sheet.

(Eq. 11)

The stomata resistance is a physiological quantity for which there are empirical relationships to physical environmental variables that were previously derived from micrometeorological and ecophysiological field measurements.

As an example of a parameterization for the *r _{s}* of a forest stand is given by Wesely et al. (1989) as follows:

Q is the global radiation in W / m^{2} and with T the leaf temperature in ° C. The two factors [Q] and [T] stand for the unit of global radiation or the leaf temperature. As a result of the multiplication, these terms of the empirical model become unitless. For all other conditions (at night) only cuticular evaporation is assumed (e.g. *r _{s}* = 2000 s / m).

Wesely, M.L., Sisteron, D.L. and Jastrow, J.D., 1989. Parameterization of surface resistance to gaeous dry deposition in regional-scale numerical models. Atmospheric Environment, 23 (6): 1293-1304.

There are a number of other parameterizations from which this was only selected for reasons of ease of use. At this point, it is strongly warned against viewing this parameterization as generally valid.

*Monteith, J.L. (1965): Evaporation and environment (Ed.): The state and movement of water in living organisms, Symposia of the Society for Experimental Biology. Cambridge University Press, 205-234.*

You can find exercises for this unit here.

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Last change on 01/22/2001

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